Rounded corners in TikZ trees.THANKS to Andrew for raising interest in this question by adding the bounty (I had exactly the same problem and asked for help in the chat) and of course to Saso for coding this solution!

Rounded corners in TikZ trees.This is a fast and simple way to achieve the desired effect. However, if you have several nodes in various relations to each other or with different values of rounded corners it requires a lot of manual work.